#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define N 1000000000

int main() {
  double a1 = 0.3431457505076198047932451031, y1 = 0.4142135623730950488016887242096980, a2, y2, aux;
  int i, exp;
  for (i=0; i<N; i++) {
    aux = pow( 1.0 - pow(y1, 4), 0.25);
    y2 = (1.0 - aux) / (1.0 + aux);
    exp = i < 500 ? 2*i+3 : 1003;
    a2 = a1*pow(1+y2, 4) - pow(2, exp)*y2*(1.0+y2+y2*y2);
    a1 = a2;
    y1 = y2;
  }
  printf("%.06lf\n", 1.0/a2);

  return 0;
}
